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Free Grade 3 Expanded Form Lessons

Free Grade 3 lessons for Expanded Form: 12 real questions with a full answer key and worked solutions. An expression uses letters for numbers. Substitute a value to evaluate it, collect like terms to simplify it, and multiply every term in a bracket to expand it.

Price

Free

Difficulty

Foundation

Estimated time

20 min

Total marks

24

Learning objectives

Every objective is checkable, and each one maps to an activity and an assessment.

  • RememberIdentify expanded form

    Identify expanded form accurately in a familiar context.

    Assessed by: Exit ticket of four short items

  • UnderstandExplain expanded form

    Explain expanded form accurately in a familiar context.

    Assessed by: Exit ticket of four short items

  • ApplyCalculate expanded form

    Calculate expanded form accurately in a familiar context.

    Assessed by: Exit ticket of four short items

  • AnalyseCompare expanded form

    Compare expanded form accurately in a familiar context.

    Assessed by: Exit ticket of four short items

Prerequisites

Close these gaps first — each has its own free lesson, worksheet and quiz.

The Number Line
Ordering Numbers

How Expanded Form works

An expression uses letters for numbers. Substitute a value to evaluate it, collect like terms to simplify it, and multiply every term in a bracket to expand it.

Key wordsexpressiontermlike termssubstituteexpand

12 practice questions

Easy to hard, 24 marks in total. Try them first, then open the answers.

  1. 1.Find the value of 6x + 13 when x = 6.[1]
  2. 2.Find the value of 2x + 16 when x = 5.[1]
  3. 3.Find the value of 4x + 10 when x = 9.[1]
  4. 4.Find the value of 9x + 3 when x = 7.[1]
  5. 5.Simplify 8x + 3y + 3x − 5y.[2]
  6. 6.Simplify 5x + 7y + 3x − 2y.[2]
  7. 7.Simplify 2x + 3y + 9x − 2y.[2]
  8. 8.Simplify 4x + 1y + 4x − 6y.[2]
  9. 9.Expand 3(4x + 8).[3]
  10. 10.Expand 4(2x + 8).[3]
  11. 11.Expand 2(5x + 9).[3]
  12. 12.Expand 2(4x + 2).[3]
Show answers and working

  1. 1. 49

    Replace x with 6: 6 × 6 + 13. 36 + 13 = 49.

  2. 2. 26

    Replace x with 5: 2 × 5 + 16. 10 + 16 = 26.

  3. 3. 46

    Replace x with 9: 4 × 9 + 10. 36 + 10 = 46.

  4. 4. 66

    Replace x with 7: 9 × 7 + 3. 63 + 3 = 66.

  5. 5. 11x − 2y

    Collect x terms: 8x + 3x = 11x. Collect y terms: 3y − 5y = -2y.

  6. 6. 8x + 5y

    Collect x terms: 5x + 3x = 8x. Collect y terms: 7y − 2y = 5y.

  7. 7. 11x + 1y

    Collect x terms: 2x + 9x = 11x. Collect y terms: 3y − 2y = 1y.

  8. 8. 8x − 5y

    Collect x terms: 4x + 4x = 8x. Collect y terms: 1y − 6y = -5y.

  9. 9. 12x + 24

    Multiply each term inside by 3. 3 × 4x = 12x, 3 × 8 = 24.

  10. 10. 8x + 32

    Multiply each term inside by 4. 4 × 2x = 8x, 4 × 8 = 32.

  11. 11. 10x + 18

    Multiply each term inside by 2. 2 × 5x = 10x, 2 × 9 = 18.

  12. 12. 8x + 4

    Multiply each term inside by 2. 2 × 4x = 8x, 2 × 2 = 4.

Worked examples

Easy example

Find the value of 5x + 15 when x = 2.

  1. Replace x with 2: 5 × 2 + 15.
  2. 10 + 15 = 25.
  3. Answer: 25
Medium example

Simplify 2x + 3y + 9x − 8y.

  1. Collect x terms: 2x + 9x = 11x.
  2. Collect y terms: 3y − 8y = -5y.
  3. Answer: 11x − 5y
Hard example

Expand 3(2x + 1).

  1. Multiply each term inside by 3.
  2. 3 × 2x = 6x, 3 × 1 = 3.
  3. Answer: 6x + 3

Interactive practice

Free, no account required — answer on screen or print it.

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Common mistakes

What learners typically get wrong, and how to fix it.

  • Reads 3x as 3 + x, or as 3 with x stuck on.

    Correction: 3x means 3 × x.

  • Only multiplies the first term when expanding.

    Correction: Draw arrows from the outside to every inside term.

Teacher tips

  • · Use algebra tiles to show collecting like terms.

Parent tips

  • · Ask what 'number of pizzas × price' is for different orders.

Real-life applications

  • · Formulas for cost: total = 5n + 2 for n items plus delivery.

Assessment objectives

How mastery is evidenced, and which standards it maps to.

AQA AQA-893.1 — Mapped statement covering Expanded Form.FBISE FBI-499.2 — Mapped statement covering Expanded Form.

Every free resource for Expanded Form

One concept, one ecosystem — all of it free.

Free Expanded Form worksheets
Free Expanded Form quizzes
Free Expanded Form flashcards
Free Expanded Form lesson plans

Goes deeper

The entities below this one, each with the same complete free resource set.

Introducing Expanded Form
Working with Expanded Form
Expanded Form in Context

Sibling concepts

Reading Whole Numbers
Place Value
Digits
Comparing Numbers
Ordering Numbers
The Number Line
Standard Form
Word Form

Related concepts

Lateral links, including across subjects.

Reading Whole Numbers
Place Value
Digits
Comparing Numbers
Ordering Numbers
The Number Line
Number Formation

Next topics

Standard Form
Word Form
Rounding
Estimation

All free formats for this concept

Every kind below is a real page, generated from this entity.

Frequently asked

Is this Grade 3 Expanded Form lesson really free?
Yes. Every lessons on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
What should a learner already know before this?
Start with The Number Line, Ordering Numbers. Each one has its own free lesson, worksheet and quiz.
How is the lesson sequenced?
Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
What comes next after Expanded Form?
Move on to Standard Form, Word Form, Rounding, Estimation, which build directly on this idea.

Related resources

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